Artykuły (WMI)https://repozytorium.umk.pl:443/handle/item/802024-03-29T14:22:26Z2024-03-29T14:22:26ZAnaliza formuły emerytalnej E=K/TPlaskacz, Sławomirhttps://repozytorium.umk.pl:443/handle/item/63052020-04-27T09:39:39Z2020-04-27T00:00:00ZAnaliza formuły emerytalnej E=K/T
Plaskacz, Sławomir
Wraz z reformą emerytalną z roku 1999 zmienił się zasadniczo sposób naliczania wysokości emerytury. Emeryturę E nalicza się według prostego wzoru:
E=K/T,
gdzie K jest sumą zwaloryzowanych składek emerytalnych oraz zwaloryzowanego kapitału emerytalnego, a T jest średnią dalszą długością trwania życia wyrażoną w miesiącach. W pracy zaproponowany jest alternatywny sposób naliczania wysokości emerytury, który także opiera się na wielkościach K oraz T. Zaproponowana formuła uwzględnia ponadto dodatnią stopę procentową(techniczną stopą procentową) równą średniej realnej stopie waloryzacji świadczeń w okresie ostatnich dwudziestu lat. W rezultacie przyjęcia proponowanej formuły wysokość emerytury jest znacząco wyższa w momencie przechodzenia na emeryturę, co w istotny sposób podnosi stopy zastąpienia. Jednocześnie waloryzacja emerytur zostaje ograniczona do waloryzacji o wskaźnik inflacji, dzięki czemu zaproponowana zmiana nie wpływa zasadniczo na finanse ZUS.; The method of calculating pensions in Poland has essentially changed along with the pension system reform in 1999. Along with the new rules, an E pension is calculated with the use of a simple formula
E=K/T,
where K is the sum of indexed pension contributions and indexed initial capital and T is an average future lifetime measured in months as calculated on the basis of the Polish Life Expectancy Tables for women and men together. In the paper, a variant formula for pension calculation is proposed. The new formula is based upon the same K and T quantities. The proposed formula takes into account a positive interest rate referred to as the technical interest rate in actuarial mathematics. In the paper, the interest rate is equal to the average real annual rate of benefits indexation over the last 20 years. As a consequence of application the proposed formula, it would be necessary to reduce the benefits indexation rate to the inflation rate. However, the pension level would be higher at the moment of retirement and, in turn, the substitution level would also be higher. In essence, the proposed changes have no effects upon the financial condition of ZUS [Social Security Institution].
2020-04-27T00:00:00ZThe structure and homological properties of generalized standard Auslander-Reiten componentsMalicki, PiotrSkowroński, Andrzejhttps://repozytorium.umk.pl:443/handle/item/49112018-02-09T00:20:20Z2018-02-08T00:00:00ZThe structure and homological properties of generalized standard Auslander-Reiten components
Malicki, Piotr; Skowroński, Andrzej
We describe the structure and homological properties of arbitrary generalized standard Auslander-Reiten components of artin algebras. In particular, we prove that for all but finitely many indecomposable modules in such components the Euler characteristic is defined and nonnegative. Further, we provide a handy criterion for an infinite Auslander-Reiten component of an artin algebra to be generalized standard. We solve also the long standing open problem concerning the structure of artin algebras admitting a separating family of Auslander-Reiten components.
2018-02-08T00:00:00ZCOMPOSITION OF IRREDUCIBLE MORPHISMS IN QUASI-TUBESChaio, ClaudiaMalicki, Piotrhttps://repozytorium.umk.pl:443/handle/item/47872018-01-09T00:20:21Z2017-01-01T00:00:00ZCOMPOSITION OF IRREDUCIBLE MORPHISMS IN QUASI-TUBES
Chaio, Claudia; Malicki, Piotr
We study the composition of irreducible morphisms between indecomposable modules lying in quasi-tubes of the Auslander-Reiten quivers of artin algebras in relation with the powers of the radical of their module category.
2017-01-01T00:00:00ZOn ergodicity of foliations on $\mathbb Z^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lensesFrączek, KrzysztofSchmoll, Martinhttps://repozytorium.umk.pl:443/handle/item/47682017-12-28T00:20:43Z2017-12-27T00:00:00ZOn ergodicity of foliations on $\mathbb Z^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses
Frączek, Krzysztof; Schmoll, Martin
We consider the geodesic flow defined by periodic Eaton lens patterns in the plane and discover ergodic ones among those. The ergodicity result on Eaton lenses is derived from a result for quadratic differentials on the plane that are pull backs
of quadratic differentials on tori. Ergodicity itself is concluded for $\mathbbZ^d$-covers of quadratic differentials on compact surfaces with vanishing Lyapunov exponents.
2017-12-27T00:00:00ZErgodic properties of the ideal gas model for infinite billiardsFrączek, Krzysztofhttps://repozytorium.umk.pl:443/handle/item/47672017-12-28T00:20:44Z2017-12-27T00:00:00ZErgodic properties of the ideal gas model for infinite billiards
Frączek, Krzysztof
In this paper we study ergodic properties of the Poisson suspension (the ideal gas model) of the billiard flow $(b_t)_{t\in\mathbb R}$ on the plane with a $\Lambda$-periodic pattern ($\Lambda\subset\mathbb R^2$ is a lattice) of polygonal scatterers. We prove that if the billiard table is additionally rational then for a.e. direction $\theta\in S^1$ the Poisson suspension of the directional billiard flow $(b^\theta_t)_{t\in\mathbb R}$ is weakly mixing. This gives the weak mixing of the Poisson suspension of $(b_t)_{t\in\mathbb R}$. We also show that for a certain class of such rational billiards (including the periodic version of the classical
wind-tree model) the Poisson suspension of $(b^\theta_t)_{t\in\mathbb R}$ is not mixing for a.e. $\theta\in S^1$.
2017-12-27T00:00:00ZNonlinear time-harmonic Maxwell equations in an anisotropic bounded mediumMederski, JarosławBartsch, Thomashttps://repozytorium.umk.pl:443/handle/item/41122017-03-20T11:12:24Z2017-03-18T00:00:00ZNonlinear time-harmonic Maxwell equations in an anisotropic bounded medium
Mederski, Jarosław; Bartsch, Thomas
2017-03-18T00:00:00ZKrull Dimension of Tame Generalized Multicoil AlgebrasMalicki, Piotrhttps://repozytorium.umk.pl:443/handle/item/40772017-02-22T06:45:38Z2015-01-01T00:00:00ZKrull Dimension of Tame Generalized Multicoil Algebras
Malicki, Piotr
We determine the Krull dimension of the module category of finite dimensional tame generalized multicoil algebras over an algebraically closed field, which are domestic.
2015-01-01T00:00:00ZFinite cycles of indecomposable modulesMalicki, PiotrPena, Jose AntonioSkowroński, Andrzejhttps://repozytorium.umk.pl:443/handle/item/23672015-01-13T00:20:10Z2013-11-25T00:00:00ZFinite cycles of indecomposable modules
Malicki, Piotr; Pena, Jose Antonio; Skowroński, Andrzej
We solve a long standing open problem concerning the structure of finite cycles in the category $\mo A$ of finitely generated modules over an arbitrary artin algebra $A$, that is, the chains of homomorphisms $M_0 \buildrel {f_1}\over {\hbox to 6mm{\rightarrowfill}} M_1 \to \cdots \to M_{r-1} \buildrel {f_r}\over {\hbox to 6mm{\rightarrowfill}} M_r=M_0$ between indecomposable modules in $\mo A$ which do not belong to the infinite radical of $\mo A$. In particular, we describe completely the structure of an arbitrary module category $\mo A$ whose all cycles are finite. The main structural results of the paper allow to derive several interesting combinatorial and homological properties of indecomposable modules lying on finite cycles. For example, we prove that for all but finitely many isomorphism classes of indecomposable modules $M$ lying on finite cycles of a module category $\mo A$ the Euler characteristic of $M$ is well defined and nonnegative. Moreover, new types of examples illustrating the main results of the paper are presented.
2013-11-25T00:00:00ZEigenvalue Spectra of Functional Networks in fMRI Data and Artificial ModelsPiersa, JarosławZając, Katarzynahttps://repozytorium.umk.pl:443/handle/item/16822014-02-12T00:20:12Z2013-06-09T00:00:00ZEigenvalue Spectra of Functional Networks in fMRI Data and Artificial Models
Piersa, Jarosław; Zając, Katarzyna
In this work we provide a spectral comparison of functional networks in fMRI data of brain activity and artificial energy-based neural model. The spectra (set of eigenvalues of the graph adjacency matrix) of both networks turn out to obey similar decay rate and characteristic power-law scaling in their middle parts. This extends the set of statistics, which are already confirmed to be similar for both neural models and medical data, by the graph spectrum.
Full paper available at Springerlink:
http://link.springer.com/chapter/10.1007%2F978-3-642-38658-9_19
2013-06-09T00:00:00ZSpectra of the Spike-Flow Graphs in Geometrically Embedded Neural NetworksPiersa, JarosławSchreiber, Tomaszhttps://repozytorium.umk.pl:443/handle/item/16742014-02-09T10:32:20Z2012-04-29T00:00:00ZSpectra of the Spike-Flow Graphs in Geometrically Embedded Neural Networks
Piersa, Jarosław; Schreiber, Tomasz
In this work we study a simplified model of a neural activity flow in networks, whose connectivity is based on geometrical embedding, rather than being lattices or fully connected graphs. We present numerical results showing that as the spectrum (set of eigenvalues of adjacency matrix) of the resulting activity-based network develops a scale-free dependency. Moreover it strengthens and becomes valid for a wider segment along with the simulation progress, which implies a highly organised structure of the analysed graph.
Full article available at Springerlink:
http://link.springer.com/chapter/10.1007%2F978-3-642-29347-4_17
DOI:
10.1007/978-3-642-29347-4_17
2012-04-29T00:00:00Z